Here in the UK, you can go before a sort of judicial committee to do it, the Gender Recognition Panel; costs like £140ish. It's kind of a pain; you need to be at least 2 years in full-time, it does help if you've had SRS or at the very least are going to (and they're going to want medical reports), and you'll need two medical practitioners (one of which must be recognised in a list as a psychiatrist or psychologist specialising in gender dysphoria) to testify that yes, you are trans, yes, really you're not going to change your mind, and this is what you've done/are going to do about it. If you pass (and it's a little bizarre and intimidating that they're judging this), you get a new short birth certificate (and can apply for a long one, and thereafter a passport under your new official identity); you then have two proper birth certificates, the historical document you were born with, and a brand new one listing only your target gender (and name). The fact that you have done all this is confidential (unless you tell someone, obviously).

Your mileage will vary, naturally.

  and it kind of seems like rewriting History if ex-colleagues talk about X-woman as X-woman in the past when she was not yet X-woman but Y-guy instead

I'm a 38 year-old male who has never had gender identity issues so here's what I do to empathize. I imagine that I was forced to dress like a woman and given a female name for the first 20 or 30 years of my life. That would have been a painful time. Additionally, I imagine that a lot of people think that I'm a freak for wanting to be treated as a man today.

When I put myself into those shoes... I can imagine how it would be incredibly reassuring/reaffirming just to hear people refer to me as "John" whenever possible, even when referring to times when I was forced to dress like a woman, since I was really "John" inside all that time anyway.